Reminders and Time Zones

I live in Ohio, the eastern time zone. I have a reminder set for 6AM to take my meds. I often travel to Houston, in the Central time zone, and while in Houston my reminder goes off at 5AM, which is 6AM in Ohio. This has been going on for several years, multiple iPhones and iOS versions, and I'm finally trying to find out why. I thought the reminder's time setting was supposed to adjust for time zones, so my above 6AM alarm would go off at 6AM no matter where I was. Looking forward to any help you can give.